Mathematical Physics

Title:
Towards a state minimizing the output entropy of a tensor product of random quantum channels

Abstract: We consider the image of some classes of bipartite quantum states under a
tensor product of random quantum channels. Depending on natural assumptions
that we make on the states, the eigenvalues of their outputs have new
properties which we describe. Our motivation is provided by the additivity
questions in quantum information theory, and we build on the idea that a Bell
state sent through a product of conjugated random channels has at least one
large eigenvalue. We generalize this setting in two directions. First, we
investigate general entangled pure inputs and show that that Bell states give
the least entropy among those inputs in the asymptotic limit. We then study
mixed input states, and obtain new multi-scale random matrix models that allow
to quantify the difference of the outputs' eigenvalues between a quantum
channel and its complementary version in the case of a non-pure input.